Sharp EL-512: Lorentz Factor, Table, Geometric Mean, 3D Vectors
Blog entries now made in Windows 11.
Today’s blog will feature the classic Sharp EL-512 from the 1980s. The Sharp EL-512 is a keystroke programming calculator. The EL-512 has four program slots with a memory of 128 programming steps. All programs on the EL-512 are “entered in the blind” and must be entered in full each time.
Program commands:
[ x ]: prompt for a number. When editing a program, we will need to enter a valid number to continue the program.
LOOK: Stops the program and shows the immediate results.
Memory and recall:
STO: Stores the number in the display to memory register 1-9
x → M: Store the number in the display to memory M
M+: add to memory M
RM: recall memory M
Kn:
After a clear or an arithmetic key, just recalls the contents of memory register 1-9.
After entering a number, multiplies the number in the display by the contents of the memory register 1-9 (like RCL× K#)
To recall a register without alteration, it is always safe to multiply the register by 1:
1 Kn #
My review from 2020:
https://edspi31415.blogspot.com/2020/09/retro-review-sharp-el-512-scientific.html
Lorenz Factor
LF = (√(1-v²/c²))⁻¹
c = Speed of light in a vacuum = 299,792,452 m/s
Program:
x²
÷
299792458
x²
+/-
1
=
√
1/x
Examples:
v = 2.1E8 (2.1 * 10^8) m/s; Result: 1.401212716
v = 2,456,000 m/s; Result: 1.000033559
v = 1,000,000 m/s; Result: 1.060752
Table: Quadratic Polynomial
Generate a table using the function:
f(x) = K3 × x² + K2 × x + K1
where x increases by 1.
Before running the program, store the following:
x² coefficient: K3
x coefficient: K2
constant coefficient: K1
beginning value: Subtract 1, then store the starting value in M. For example, if we want to start with x = 1, store 0 in M.
Program:
1
M+
RM
x²
Kn 3
+
RM
Kn 2
+
1
Kn 1
=
Example:
f(x) = 0.3 × x² + 4 × x – 2.01
Start with x = 1
0.3 STO 3
4 STO 2
-2.01 STO 1
1-1 = 0 x→M
Run the program:
f(1) = 2.29
f(2) = 7.19
f(3) = 12.69
f(4) = 18.79
f(5) = 25.49
Geometric Mean
This program calculates the geometric mean (Π(x_i)^(1/n)) by the formula:
GM = 1/n × Σ(ln x_i) (x≠0)
This will require two program slots, so I’m using program slots 1: and 2:.
Memory registers used:
K1 = Σ(ln x_i)
M = n
Steps:
1. Store 0 to memory M (x→M) and memory 1 (STO 1)
2. Enter x_i and press 1:. Continue until you enter all the data. The number of data points is shown.
3. Press 2: to get the geometric mean.
Program 1:
ENT (enter a valid number)
LN
+
Kn 1
=
STO 1
1
M+
RM
Program 2:
RM
1/x
Kn 1
e^x
Example:
Find the geometric mean of 4, 9, 3, 7, 2, 8, 8, 5, and 6. 9 data points.
0 x→M, 0 STO 1
4 [1:], 9 [1:], 3 [1:], 7 [1:], 2 [1:], 8 [1:], 8 [1:], 5 [1:], 6 [1:]
[2:]
Result (geometric mean): 5.2254102087
3D Vectors: Norm of Two Vectors, Dot Product, Angle between Vectors
For this, I presume that the calculator is set to the desired angle setting (DRG). For the example, I have the EL-512 set to degree mode.
Store the vectors as follows:
First vector: [ register 1, register 2, register 3 ]
Second vector: [ register 4, register 5, register 6 ]
The program returns four values:
Norm of the first vector, stored in register 7
Norm of the second vector, stored in register 8
Dot product, stored in registered in M
Angle between two vectors, stored in register 9
Program:
1
Kn 1
↕
1
Kn 2
→rθ
↕
1
Kn 3
→rθ
STO 7
LOOK
1
Kn 4
↕
1
Kn 5
→rθ
↕
1
Kn 6
→rθ
STO 8
LOOK
1
Kn 1
Kn 4
x→M
1
Kn 2
Kn 5
M+
1
Kn 3
Kn 6
M+
RM
LOOK
÷
(
1
Kn 7
Kn 8
)
=
cos⁻¹
STO 9
Example:
First vector: [ 70, 64, 36 ]
Second vector: [ 55, 18, 94 ]
Results:
Norm of first vector: 101.4494948
Norm of second vector: 110.3856875
Dot product: 8386
Angle: 41.50953299°
Hope you enjoyed this trip down memory lane. Did you have or do you have a Sharp EL-512 or any similar calculator?
Eddie
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